Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Tam Nguyen Phan
Affiliation:

MPIM
Date:

Thu, 2019-05-16 15:00 - 16:00 The locally symmetric space SL(n,Z)\SL(n,R)/SO(n), or the space of flat n-tori of unit volume, has immersed, totally geodesic, flat tori of dimension (n-1). These tori are natural candidates for nontrivial homology cycles of manifold covers of SL(n,Z)\SL(n,R)/SO(n). In joint work with Grigori Avramidi, we show that some of these (n-1)-dim tori give nontrivial rational homology cycles in congruence covers of the locally symmetric space SL(n,Z) \SL(n,R)/SO(n). We also show that the dimension of the subspace of the (n-1)-homology group spanned by flat (n-1)-tori grows as one goes up in congruence covers. I will attempt to explain these in a general audience talk, which means, in this case, the prerequisite for this talk is basic linear algebra.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/9232

[4] http://www.mpim-bonn.mpg.de/node/158